Unit 1 Basics of Geometry

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Midpoint Property

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1

Midpoint Property

If (x1, y1) and (x2, y2) are the coordinates of the endpoints of a segment, then the coordinates of the midpoint are: (X plus X divided by 2, and, Y plus Y divided by 2) Labeled as a coordinate pair (X, Y).

<p>If (x1, y1) and (x2, y2) are the coordinates of the endpoints of a segment, then the coordinates of the midpoint are: (X plus X divided by 2, and, Y plus Y divided by 2) Labeled as a coordinate pair (X, Y).</p>
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2

Undefined terms of Geometry

point, line, plane

<p>point, line, plane</p>
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3

Collinear Points

points that lie on the same line

<p>points that lie on the same line</p>
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4

Coplanar Points

points that lie on the same plane

<p>points that lie on the same plane</p>
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5

Line Segment

consists of two points called the endpoints and all the points in between them that are collinear with the two points

<p>consists of two points called the endpoints and all the points in between them that are collinear with the two points</p>
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Congruent segments

segments that have the same measure or length

<p>segments that have the same measure or length</p>
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Midpoint of a segment

the point on the segment that is same distance from both endpoints, midpoint bisects the segment

<p>the point on the segment that is same distance from both endpoints, midpoint bisects the segment</p>
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Ray

Portion of a line that contains all the points on the line that are on the same side of the first letter as the second letter

<p>Portion of a line that contains all the points on the line that are on the same side of the first letter as the second letter</p>
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Angle

Two noncollinear rays having a common endpoint.

<p>Two noncollinear rays having a common endpoint.</p>
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Adjacent Angles

two angles that share a common vertex and side, but have no common interior points

<p>two angles that share a common vertex and side, but have no common interior points</p>
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Measure of an angle

the smallest amount of rotation about the vertex from one ray to the other.

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Protractor

a geometry tool used to measure angles

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13

Congruent Angles

two angles that have the same measure

<p>two angles that have the same measure</p>
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14

Angle Bisector

a ray that contains the vertex and divides the angle into two congruent angles

<p>a ray that contains the vertex and divides the angle into two congruent angles</p>
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Counterexample

an example that proves that a statement is false

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16

Parallel Lines

lines in the same plane that never intersect

<p>lines in the same plane that never intersect</p>
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Perpendicular Lines

lines that intersect at right angles (90 degrees)

<p>lines that intersect at right angles (90 degrees)</p>
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Skew Lines

lines that are not in the same plane and do not intersect

<p>lines that are not in the same plane and do not intersect</p>
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Acute Angle

an angle that measures greater than 0 degrees and less than 90 degrees

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Right Angle

an angle that measures 90 degrees

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Obtuse Angle

An angle that measures more than 90 degrees but less than 180 degrees

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Straight Angle

an angle that measures 180 degrees

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Linear Pair

two adjacent angles whose noncommon sides are opposite rays

<p>two adjacent angles whose noncommon sides are opposite rays</p>
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Vertical Angles

angles formed by 2 intersecting lines; they share a common vertex not a side

<p>angles formed by 2 intersecting lines; they share a common vertex not a side</p>
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Complementary Angles

two angles whose measures have a sum of 90 degrees

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supplementary angles

two angles whose measures have a sum of 180 degrees

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Polygon

a closed figure in a plane, formed by connecting line segments endpoint to endpoint with each segment intersecting exactly two others

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Three Sided Polygon

Triangle

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Four Sided Polygon

quadrilateral

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Five Sided Polygon

pentagon

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Six Sided Polygon

hexagon

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Seven Sided Polygon

heptagon

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Eight Sided Polygon

octagon

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Nine Sided Polygon

nonagon

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Ten Sided Polygon

decagon

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Eleven Sided Polygon

undecagon

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Twelve Sided Polygon

dodecagon

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diagonal of a polygon

a line segment connecting two nonconsecutive vertices of a polygon

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convex polygon

a polygon with no diagonal outside the polygon

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Concave Polygon

A polygon that has at least one diagonal with points outside the polygon.

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congruent polygons

two polygons whose corresponding sides and angles are congruent

<p>two polygons whose corresponding sides and angles are congruent</p>
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equilateral polygon

a polygon in which all sides are congruent

<p>a polygon in which all sides are congruent</p>
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equiangular polygon

A polygon with all angles have same measure

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Regular Polygon

a polygon that is both equilateral and equiangular

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Right Triangle

a triangle that has one right angle

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acute triangle

A triangle with 3 acute angles

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obtuse triangle

a triangle with one obtuse angle

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scalene triangle

a triangle with no congruent sides

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equilateral triangle

A triangle with three congruent sides

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Isosceles Triangle

a triangle with at least two congruent sides

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<p>Trapezoid</p>

Trapezoid

A quadrilateral with exactly one pair of parallel sides

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<p>Kite</p>

Kite

a quadrilateral with two distinct pairs of consecutive congruent sides

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<p>Parallelogram</p>

Parallelogram

A quadrilateral with two pairs of parallel sides

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<p>Rhombus</p>

Rhombus

an equilateral parallelogram (all congruent sides, 2 pairs of parallel sides)

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<p>Rectangle</p>

Rectangle

an equiangular parallelogram (all congruent angles, 2 pairs of parallel sides)

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<p>Square</p>

Square

an equilateral rectangle or an equiangular rhombus or a regular quadrilateral

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Circle

The set of all points in a plane that are the same distance from a given point called the center

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Radius

The distance from the center of a circle to any point on the edge of a circle

<p>The distance from the center of a circle to any point on the edge of a circle</p>
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Diameter

A line segment that passes through the center of a circle and has endpoints on the circle

<p>A line segment that passes through the center of a circle and has endpoints on the circle</p>
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Secant

A line that intersects a circle in two points

<p>A line that intersects a circle in two points</p>
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chord

A segment whose endpoints lie on a circle

<p>A segment whose endpoints lie on a circle</p>
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Tangent

A line in the plane of a circle that intersects the circle in exactly one point.

<p>A line in the plane of a circle that intersects the circle in exactly one point.</p>
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point of tangency

the point where a circle and a tangent intersect

<p>the point where a circle and a tangent intersect</p>
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congruent circles

Two or more circles that have the same radius

<p>Two or more circles that have the same radius</p>
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concentric circles

2 or more coplanar circles with the same center

<p>2 or more coplanar circles with the same center</p>
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arc of a circle

two points on the circle and the continuous part of the circle between the two points

<p>two points on the circle and the continuous part of the circle between the two points</p>
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semicircle

an arc with endpoints that are the endpoints of a diameter

<p>an arc with endpoints that are the endpoints of a diameter</p>
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minor arc

an arc that is less than a semicircle

<p>an arc that is less than a semicircle</p>
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Major Arc

an arc that is greater than a semicircle

<p>an arc that is greater than a semicircle</p>
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70

Central Angle

an angle with its vertex at the center of a circle

<p>an angle with its vertex at the center of a circle</p>
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arc measure

the measure of the corresponding central angle

<p>the measure of the corresponding central angle</p>
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